EP2491760B1 - Process for induction heating used used in a device incorporating magnetically coupled inductors - Google Patents

Description

The present invention relates to a method of induction heating implemented in a heating device of a metal part such as a metal sheet or a bar, the device comprising magnetically coupled inductors. By magnetic coupling is meant that the inductors produce between them mutual inductions.

The most conventional induction heating techniques implement configurations that are satisfactory when the parts to be heated are always of the same nature and dimensions. But the industry demands more and more flexibility and productivity. The production lines are required to adapt in continuous operation to the change of the position or the format of the parts to be heated, and to adapt according to this change the desired temperature profile.

Known technologies make it possible to control heating by zone of injected power, but the control of the temperature profile in the heated zones remains linked to the geometrical design of the coils and to their mode of supply, mainly by the variation of amplitude of the currents that we inject. The determination of these currents and the resulting regulation is highly dependent on the magnetic coupling existing between the coils due to the mutual inductions, each energized coil having an influence on all the others. Magnetic coupling makes the control of the temperature profile of the heated part extremely delicate, without counting that it can have harmful repercussions on the frequency generators, for example a breakage of components.

The patent application WO 00/28787 A1 discloses a system for heating a tubular metal part by induction coils fed via a dimmer type interrupt circuit connected to an inverter type power source. A control circuit makes it possible to vary the duration of the power injected by the power source to each coil in order to heat different different zones of the metal part differently in view of a desired temperature profile. The injection of power into a coil is therefore done in "all or nothing", that is to say, it can be prevented on a cycle corresponding to several periods of the This system nevertheless has drawbacks, and in particular it makes it possible to control only the average power produced by each coil without being able to precisely control the temperature profile generated by the coils in the heated room. In addition, it is apparent from this document that the connection of the coils and the inverters must be to a certain extent defined according to the load and the temperature profile to be achieved. Moreover, this document does not mention the magnetic couplings between the circuits nor how to get rid of them or to take them into account.

The present invention aims to solve these disadvantages and to provide a heating method taking into account the many couplings, on the one hand between the different inductors and on the other hand between the inductors and the part to be heated, to allow control with a good accuracy the temperature profile generated by the inductors. The invention aims in particular to be able to adjust the heating to different desired temperature profiles in real time, by acting on the control of inverters supplying the inductors and without the need to adjust the structure of the inductors.

1. a) on compare ledit profil de température effectif à un profil de température de référence, et on calcule un profil de densité de puissance de référence que le dispositif de chauffage doit injecter dans ladite pièce pour atteindre ledit profil de température de référence ;
2. b) à partir d'une matrice d'impédances déterminée par la connaissance des relations électromagnétiques liant lesdits inducteurs entre eux et à ladite pièce et par la connaissance de fonctions images vectorielles représentatives des relations liant les densités de courant créées par les inducteurs aux courants traversant les inducteurs, on calcule des courants cibles que doivent délivrer les onduleurs afin que les courants des inducteurs atteignent des valeurs cibles appropriées pour injecter dans ladite pièce ledit profil de densité de puissance de référence ;
3. c) on détermine les courants traversant les inducteurs pour les comparer aux dites valeurs cibles et déterminer des écarts de courants à corriger, et on envoie aux dites unités de commande des instructions de correction en fonction desdits écarts de courants afin de commander les onduleurs de façon à corriger les courants traversant les inducteurs.

For this purpose, the subject of the invention is an induction heating method implemented in a device for heating a metal part, the device comprising magnetically coupled inductors, each inductor being powered by a specific inverter and associated with a capacitor to form an oscillating circuit, said oscillating circuits having at least approximately the same resonance frequency, each inverter being controlled by a control unit so as to vary the amplitude and phase of the current flowing through the corresponding inductor , the device further comprising means for determining said current as well as means for determining an effective temperature profile of said metal part, said method comprising the following steps:

1. a) comparing said actual temperature profile to a reference temperature profile, and calculating a reference power density profile that the heater is to inject into said room to achieve said reference temperature profile;
2. b) from an impedance matrix determined by the knowledge of the electromagnetic relations linking said inductors to each other and to said part and by the knowledge of vectorial image functions representative of the relationships linking the current densities created by the inductors to the currents passing through inductors, target currents to be supplied by the inverters are calculated so that the currents of the inductors reach appropriate target values for injecting into said part said reference power density profile;
3. c) the currents passing through the inductors are determined in order to compare them with said target values and to determine current differences to be corrected, and control commands are sent to said control units as a function of said current differences in order to control the inverters in a to correct the currents passing through the inductors.

Thanks to these provisions, we obtain a precise control of the temperature profile applied to the heated room, which is ideal for heating with the same device several pieces of different sizes and natures.

• on détermine les capacités desdits condensateurs, et on associe ladite matrice d'impédances à un vecteur des capacités ;
• on détermine une valeur initiale de ladite matrice d'impédances pour une température moyenne initiale donnée desdits inducteurs et de ladite pièce, puis on détermine à intervalles variables ou périodiques la matrice d'impédances modifiée pour au moins une valeur augmentée de ladite température moyenne, et on utilise ladite matrice d'impédances modifiée pour recalculer les dites valeurs cibles ;
• après avoir effectué successivement les étapes (a) et (b) on effectue au moins une fois l'étape (c) pour diminuer lesdits écarts de courants à corriger, puis on réitère au moins une fois les étapes (a), (b) et (c) en actualisant ledit profil de température effectif par des mesures de température en différentes zones chauffées de la pièce ;
• pour la détermination par calcul des dites valeurs cibles à l'étape (b), grâce à la connaissance desdites fonctions images vectorielles, on calcule des fonctions images des densités de puissance selon les caractéristiques spatiales des zones de la pièce dans lesquelles lesdites densités de puissance sont injectées, et on calcule un vecteur optimisé des courants cibles à déterminer en minimisant la différence entre chacune desdites fonctions images des densités de puissance et une fonction densité de puissance de référence correspondant audit profil de densité de puissance de référence ;
• on prend comme onduleur de référence un onduleur ayant par rapport aux autres onduleurs le plus fort courant dans le cas d'un onduleur de courant ou la plus forte tension dans le cas d'un onduleur de tension, et on introduit des angles de décalage sur les commandes des autres onduleurs par rapport à un angle de commande sur l'onduleur de référence ;
• on règle l'onduleur de référence avec un rapport cyclique égal à 2/3, afin de diminuer les perturbations harmoniques créées par cet onduleur sur ces voisins ;
• on règle la valeur efficace du courant dans ledit onduleur de référence en agissant sur une alimentation continue qui alimente les onduleurs.

In preferred embodiments of a heating method according to the invention, use is made in particular of one or other of the following provisions:

• the capacitances of said capacitors are determined, and said impedance matrix is associated with a capacitance vector;
• an initial value of said impedance matrix is determined for a given initial average temperature of said inductors and said part, and then the modified impedance matrix is determined at variable or periodic intervals for at least one value increased by said average temperature, and said modified impedance matrix is used to recalculate said target values;
• after successively performing steps (a) and (b), step (c) is carried out at least once to reduce said differences in currents to be corrected, and then steps (a), (b) are repeated at least once and (c) updating said effective temperature profile by temperature measurements in different heated areas of the room;
• for the determination by calculation of said target values in step (b), by virtue of the knowledge of said vector image functions, image functions of the power densities are calculated according to the spatial characteristics of the zones of the part in which said power densities are injected, and one calculates a optimized vector of the target currents to be determined by minimizing the difference between each of said power density image functions and a reference power density function corresponding to said reference power density profile;
• as a reference inverter, an inverter having the highest current with respect to the other inverters in the case of a current inverter or the highest voltage in the case of a voltage inverter, and offset angles are introduced. the controls of the other inverters with respect to a control angle on the reference inverter;
• the reference inverter is regulated with a duty cycle equal to 2/3, in order to reduce the harmonic disturbances created by this inverter on these neighbors;
• the rms value of the current in said reference inverter is regulated by acting on a continuous supply which supplies the inverters.

• des inducteurs couplés magnétiquement, chaque inducteur étant associé à un condensateur pour former un circuit oscillant, lesdits circuits oscillants possédant au moins approximativement la même fréquence de résonance ;
• des onduleurs alimentant chacun un inducteur qui lui est propre, chaque onduleur étant commandé par une unité de commande de façon à faire varier l'amplitude et la phase du courant traversant l'inducteur correspondant ;
• caractérisé en ce qu'il comprend en outre :
  • des moyens de détermination des courants traversant les inducteurs ainsi que des moyens de détermination d'un profil de température effectif d'une pièce métallique chauffée par le dispositif ;
  • des moyens de comparaison dudit profil de température effectif par rapport à un profil de température de référence ;
  • des moyens de calcul d'un profil de densité de puissance de référence que le dispositif de chauffage doit injecter dans ladite pièce pour atteindre ledit profil de température de référence ;
  • des moyens de calcul, basés sur la connaissance d'une matrice des impédances, de courants cibles que doivent délivrer les onduleurs afin que les courants des inducteurs atteignent des valeurs cibles appropriées pour injecter dans ladite pièce ledit profil de densité de puissance de référence ;
  • des moyens de comparaison des courants traversant les inducteurs par rapport aux dites valeurs cibles, aptes à déterminer des écarts de courants à corriger, et des moyens de traitement desdits écarts de courants aptes à générer des instructions de correction envoyées aux dites unités de commande pour commander les onduleurs de façon à corriger les courants traversant les inducteurs.

The invention also relates to an induction heating device comprising:

• magnetically coupled inductors, each inductor being associated with a capacitor to form an oscillating circuit, said oscillating circuits having at least approximately the same resonance frequency;
• inverters each supplying an inductor of its own, each inverter being controlled by a control unit so as to vary the amplitude and the phase of the current flowing through the corresponding inductor;
• characterized in that it further comprises:
  • means for determining the currents flowing through the inductors as well as means for determining an effective temperature profile of a metal part heated by the device;
  • means for comparing said effective temperature profile with respect to a reference temperature profile;
  • means for calculating a reference power density profile that the heating device is to inject into said room to reach said reference temperature profile;
  • calculation means, based on the knowledge of an impedance matrix, of the target currents to be delivered by the inverters so that the inductor currents achieve appropriate target values for injecting into said part said reference power density profile;
  • means for comparing the currents traversing the inductors with respect to said target values, able to determine current differences to be corrected, and means for processing said current differences able to generate correction instructions sent to said control units for controlling the inverters so as to correct currents flowing through the inductors.

• les onduleurs sont alimentés par une même alimentation source de courant ou source de tension, et lesdits moyens de comparaison desdits courants déterminés traversant les inducteurs comprennent des unités comparatrices recevant chacune des paramètres déterminés d'un courant traversant un inducteur et des paramètres des valeurs cibles correspondantes et étant chacune reliée à une unité de traitement desdits écarts de courants, une desdites unités comparatrices recevant en outre des paramètres représentatifs de ce que délivre ladite alimentation et son unité de traitement associée étant adaptée pour générer des instructions de régulation envoyées à ladite alimentation de façon à modifier le courant ou la tension qu'elle délivre.

In preferred embodiments of a heating device according to the invention, use is made in particular of one or other of the following provisions:

• the inverters are powered by the same power supply source or voltage source, and said means for comparing said determined currents passing through the inductors comprise comparator units each receiving determined parameters of a current flowing through an inductor and parameters of the corresponding target values and each being connected to a processing unit of said current gaps, one of said comparator units further receiving parameters representative of what said power supply and its associated processing unit is adapted to generate control instructions sent to said power supply so as to to modify the current or the voltage that it delivers.

• La figure 1 représente schématiquement un premier exemple de dispositif de chauffage par induction dans lequel le procédé de chauffage selon l'invention peut être mis en oeuvre, appliqué au chauffage d'un disque métallique fixe.
• La figure 2 représente schématiquement une modélisation du système à trois inductances couplées de la figure 1, vu de l'alimentation.
• La figure 3 représente schématiquement le dispositif de chauffage par induction de la figure 1, appliqué au chauffage d'une tôle que l'on déplace.
• La figure 4 représente schématiquement un deuxième exemple de dispositif de chauffage par induction, appliqué au chauffage d'une barre métallique que l'on déplace.
• La figure 5 représente schématiquement un troisième exemple de dispositif de chauffage par induction, appliqué au chauffage d'une tôle que l'on déplace.
• La figure 6 représente schématiquement un quatrième exemple de dispositif de chauffage par induction, appliqué au chauffage d'une tôle que l'on déplace.
• La figure 7 représente schématiquement une fonction image de la densité de puissance calculée à partir d'un vecteur optimisé des courants permettant de minimiser la différence entre ladite fonction et une fonction référence de densité de puissance.
• La figure 8 représente schématiquement un premier mode de réalisation d'un dispositif de chauffage par induction selon l'invention dans lequel l'alimentation des onduleurs est une source de courant.
• La figure 9 représente schématiquement un second mode de réalisation d'un dispositif de chauffage par induction selon l'invention dans lequel l'alimentation des onduleurs est une source de tension.

Other features and advantages are apparent from the following description of non-limiting examples of embodiments, with reference to the figures in which:

• The figure 1 schematically represents a first example of induction heating device in which the heating method according to the invention can be implemented, applied to the heating of a fixed metal disc.
• The figure 2 schematically represents a modeling of the system with three coupled inductances of the figure 1 , seen from the diet.
• The figure 3 schematically represents the induction heating device of the figure 1 , applied to heating a sheet that is moved.
• The figure 4 schematically represents a second example of induction heating device, applied to the heating of a metal bar that is moved.
• The figure 5 schematically shows a third example of induction heating device, applied to the heating of a sheet that is moved.
• The figure 6 schematically shows a fourth example of induction heating device, applied to the heating of a sheet that is moved.
• The figure 7 schematically represents an image function of the power density calculated from an optimized vector of the currents making it possible to minimize the difference between said function and a reference function of power density.
• The figure 8 schematically represents a first embodiment of an induction heating device according to the invention in which the supply of the inverters is a current source.
• The figure 9 schematically represents a second embodiment of an induction heating device according to the invention in which the supply of the inverters is a voltage source.

On the figure 1 , the exemplary heating device relates to a non-magnetic metal disk configuration heated by transverse flux using three pairs of twin coils, which has the advantage of keeping the axisymmetric aspect of the problem. To ensure symmetry of the entire system, each coil placed on one side of the disk is connected in series with its twin coil on the other side to form a single inductor. In this way, the system is rotational invariant. In addition, in order to work with the linearity assumption, it will be considered that the electromagnetic materials of the system have a constant and unitary permeability. Each inductor is powered by a UPS of its own type (voltage inverter) or parallel type (inverter current).

On the figure 2 , the modeling of the system in the form of coupled inductances makes it possible to represent the various existing interactions. This modeling also allows the study of the electrical supply of the inductors and the calculation of the values of currents that must be injected.

It is necessary to determine the system impedance matrix for each proposed heating configuration to reflect the magnetic state and electrical system for a given geometry. The dimension N of the matrix is given by the number of inductors, here N = 3.

The impedance matrix must be complete to account for all coupling effects. The determination of this matrix can be complex, several analytical or numerical means, or measurements in line and continuous injection of particular signals, can be implemented.

V

: Tensions sinusoïdales aux bornes des inducteurs ;

I

: Courants dans les enroulements des inducteurs;

Z

: Matrice d'impédances du système.

Thus modeled, the general equation of the system can be written: $$\underset{}{V}=Z\mathrm{.}\underset{}{I}$$

V

: Sinusoidal voltages across the inductors;

I

: Currents in the windings of the inductors;

Z

: Matrix of impedances of the system.

ou encore : $$Z=\left[\begin{array}{ccc}{R}_{11}+j{L}_{11}\omega & R_{12}+j{L}_{12}\omega & R_{13}+j{L}_{13}\omega \\ R_{21}+j{L}_{21}\omega & R_{22}+j{L}_{22}\omega & R_{23}+j{L}_{23}\omega \\ R_{31}+j{L}_{31}\omega & R_{32}+j{L}_{32}\omega & R_{33}+j{L}_{33}\omega \end{array}\right]$$

L_mm

: représente l'inductance propre de chaque inducteur ;

L_mn = L_nm

: représente les inductances mutuelles entre inducteurs ;

R_mm

: représente les résistances propres de chaque inducteur ;

R_mn = R_nm

: représente les résistances équivalentes dues aux courants induits.

In our case, the matrix Z can be written in the form: $$Z=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="11"\; label="Z"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">Z</figure-callout>}}_{11}\left(\mathrm{<figure-callout\; id="12"\; label="\omega \; Z"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\omega \; </figure-callout>},\right)& Z_{}{}_{12}\left(\mathrm{<figure-callout\; id="13"\; label="\omega \; Z"\; filenames="imgf0001.png"\; state="\{\{state\}\}">\omega \; </figure-callout>},\right)& Z_{}{}_{13}\left(\omega \right)\\ Z_{21}\left(\omega \right)& Z_{22}\left(\omega \right)& Z_{23}\left(\omega \right)\\ Z_{31}\left(\omega \right)& Z_{32}\left(\omega \right)& Z_{33}\left(\omega \right)\end{array}\right]$$

or : $$Z=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="11"\; label="R"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">R</figure-callout>}}_{11}+j{\mathrm{The}}_{11}\omega & {\mathrm{<figure-callout\; id="12"\; label="R"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">R</figure-callout>}}_{12}+j{\mathrm{The}}_{12}\omega & {\mathrm{<figure-callout\; id="13"\; label="R"\; filenames="imgf0001.png"\; state="\{\{state\}\}">R</figure-callout>}}_{13}+j{\mathrm{The}}_{13}\omega \\ R_{21}+j{\mathrm{The}}_{21}\omega & R_{22}+j{\mathrm{The}}_{22}\omega & R_{23}+j{\mathrm{The}}_{23}\omega \\ R_{31}+j{\mathrm{The}}_{31}\omega & R_{32}+j{\mathrm{The}}_{32}\omega & R_{33}+j{\mathrm{The}}_{33}\omega \end{array}\right]$$

L _mm

: represents the inductance of each inductor;

L _mn = L _nm

represents the mutual inductances between inductors;

R _mm

: represents the own resistances of each inductor;

R _mn = R _nm

: represents the equivalent resistances due to induced currents.

With the knowledge of the electromagnetic relations between the coils and the part to be heated, it is possible to calculate the currents to be injected in each of the coils in order to obtain the desired heating.

It should be noted that different configurations or conventional calculation methods try to minimize the non-diagonal coupling terms in order to overcome the problems related to the interactions between the coils. Moreover, for many cases where the couplings are weak, the own resistances of each inductor are often large compared to the equivalent resistances due to the currents induced. The classical methods thus use a simplified matrix, that is to say not complete, which only keeps the diagonal terms. This implies a simplified regulation of the heating, but at the expense of the precise control of the temperature profile and the flexibility of the installation, in particular in the area under the coils. On the contrary, the present invention takes into account the complete impedance matrix of the system to improve the determination of the currents to be injected into the coils and thus improve the control of the temperature profile of the heated part.

• I₁ : Valeur efficace du courant dans l'inducteur Ind1, lequel courant est pris comme référence de phase ;
• I₂ et ϕ ₂ : Valeur efficace du courant dans l'inducteur Ind2, et déphasage de ce courant par rapport à I _{1 ;}
• I₃ et ϕ ₃ : Valeur efficace du courant dans l'inducteur Ind3, et déphasage de ce courant par rapport à I₁ .

In the example described, we have three inductors powered by three different current sources. The determination of the currents to be injected in each coil amounts to determining five unknown variables, the phase of the current in the inductor Ind1 serving as a reference and therefore not an unknown. Indeed, for a given sheet constituting the part to be heated, the unknowns are:

• I ₁ : rms value of the current in inductor Ind1, which current is taken as phase reference;
• I ₂ and φ ₂ : rms value of the current in inductor Ind2, and phase shift of this current with respect to I _{1 ;}
• I ₃ and φ ₃ : RMS current value Ind3, and phase shift of this current relative to I ₁ .

It is understood from the foregoing that with the complete impedance matrix taken into account in the present invention, the control of the temperature profile of the heated part must be carried out not only by controlling the amplitudes of the currents in the inductors but also by controlling the phase shifts of these currents relative to one another, which implies that each inverter is controlled so as to be able to vary the amplitude and the phase of the current flowing through the corresponding inductor.

In view of the above relations, the vector of unknowns can then be written: $$X={\left\{I_1,I_2,{\phi }_2,I_3,{\phi }_3\right\}}^T$$

It is not possible to easily determine these unknowns by the usual resolution methods. Indeed, with the exception of very simple cases, the analytical formulation linking the geometric data, the electric currents in the inductors, the spatial distribution of the electromagnetic field and the power density in all points is almost impossible with so many variables. The classical field calculation software based on digital cutting techniques of the field of study in elementary meshes makes it possible to know the distribution of the magnetic field, and consequently to calculate the power densities in the conductive parts as a function of the currents injected in the inductors. In our case, an inverse problem arises, since it is a question of knowing if there exists one or several values of the vector x making it possible to obtain a desired power density profile in the part.

ρ

: représente la masse volumique ;

C_p

: représente la capacité thermique massique ;

λ

: représente la conductivité thermique.

By the application of the heat equation, it is well known that the injected power density Dp in a conductive part gives a good image of the thermal behavior of the heated product. For example, in the case of static heating where the displacement speed of the treated material is zero, knowledge of the instantaneous temperature T of the treated material conventionally requires the temporal resolution of a simplified form of the heat equation: $$\rho \cdot {\mathrm{VS}}_p\frac{\partial T}{\partial t}=\mathit{div}\left(\lambda \cdot \mathit{gradt}\right)+\mathit{dp}$$

ρ

: represents the density;

C _p

: represents the specific heat capacity;

λ

: represents the thermal conductivity.

Solving this equation implies real-time integration, which is not very difficult. In addition, in the case of a "flash" heating, that is to say if the heating time is small so that one can neglect the thermal diffusion heat within the material during this time, the expression is further simplified in this way: $$\rho \cdot {\mathrm{VS}}_p\frac{\partial T}{\partial t}=\mathit{dp}$$

We thus obtain a classical simplified expression making it possible to connect the injected power density Dp and the elevation of the temperature. Thus, from the desired thermal profile for the heated part, the desired power density profile is obtained.

où σ représente la conductivité électrique, J représente le vecteur densité de courant défini sur le rayon r dans la pièce, J_R (r,x) et J_I (r,x) représentant les composantes réelle et imaginaire de ce vecteur en fonction du rayon de la zone considérée.In the example with reference to the figure 1 , the system is invariant along the axis of revolution of the sheet metal disk and in the thickness of the sheet. We therefore take into account only one dimension of the disc, namely the radial direction of the considered area of the disc. For the determination of the vector x of unknowns, it is known that the power density along the radius of the zone considered is calculated by the following equation: $$\mathit{dp}\left(r,x\right)=\frac{1}{\sigma }{\left|\underset{}{\mathrm{<figure-callout\; id="2"\; label="J"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">J</figure-callout>}}\right|}^2,\mathrm{is}:\mathit{dp}\left(r,x\right)=\frac{1}{\sigma }\left(J_R^2\left(r,x\right)+J_I^2\left(r,x\right)\right)$$

where σ represents the electrical conductivity, J represents the current density vector defined on the radius r in the room, J _R (r, x) and J _I (r, x) representing the real and imaginary components of this vector as a function of radius of the considered area.

The exemplary system is completely linear, that is to say in particular without ferromagnetic materials or hysteresis. We can therefore apply the superimposition theorem of sources for each of the power supplies of the three inductors. It should be noted that a similar principle can be implemented in a non-linear system. We thus obtain image functions of the current densities as a function of the radius r of the annular zone considered of the heated disk, each image function f _k being representative of the relation linking the current density J _k (r), created by an inductor, at the current I _k supplying this inductor. These image functions are vectorial and have real and imaginary components defined in the following way: $$f_{\mathit{kR}}\left(r\right)=\frac{J_{\mathit{kR}}\left(r\right)}{l_k}{f}_{\mathit{kl}}\left(r\right)=\frac{J_{\mathit{kl}}\left(r\right)}{l_k}$$

avec j² = -1, soit : $$\underline{J}\left(r,x\right)={\displaystyle \sum _{k=1}^3}\left(f_{\mathit{kR}}\left(r\right)+j{f}_{\mathit{kl}}\left(r\right)\right)\mathrm{.}\left(I_k+{\mathit{jl}}_{\mathit{kl}}\right)$$

d'où $$\underline{J}\left(r,x\right)=\underset{J_R\left(r,x\right)}{\underbrace{{\displaystyle \sum _{k=\mathit{1}}^3}\left(f_{\mathit{kR}}\left(r\right)\mathrm{.}{l}_{\mathit{kR}}-f_{\mathit{kl}}\left(r\right)\mathrm{.}{l}_{\mathit{kl}}\right)}}+j\underset{J_l\left(r,x\right)}{\underbrace{{\displaystyle \sum _{k=\mathit{1}}^3}\left(f_{\mathit{kR}}\left(r\right)\mathrm{.}{l}_{\mathit{kR}}+f_{\mathit{kl}}\left(r\right)\mathrm{.}{l}_{\mathit{kR}}\right)}}$$

Ce qui peut s'écrire aussi $$\underline{J}\left(r,x\right)=J_R\left(r,x\right)+j{J}_l\left(r,x\right)$$

Finally, in our example with three inductors, the vector calculation of the total current density induced in the annular zone of radius r of the disk can be expressed as follows: $$\underset{}{J}\left(r,x\right)={\displaystyle \underset{k=1}{\overset{3}{\Sigma }}}\left(f_{\mathit{kR}}\left(r\right)+j{f}_{\mathit{kl}}\left(r\right)\right)\mathrm{.}{l}_k\mathrm{.}{e}^{\mathit{j\phi k}},$$

with j ² = -1, that is: $$\underset{}{J}\left(r,x\right)={\displaystyle \underset{k=1}{\overset{3}{\Sigma }}}\left(f_{\mathit{kR}}\left(r\right)+j{f}_{\mathit{kl}}\left(r\right)\right)\mathrm{.}\left(I_k+{\mathit{jl}}_{\mathit{kl}}\right)$$

from where $$\underset{}{J}\left(r,x\right)=\underset{J_R\left(r,x\right)}{\underset{\}}{{\displaystyle \underset{k=\mathit{1}}{\overset{3}{\Sigma }}}\left(f_{\mathit{kR}}\left(r\right)\mathrm{.}{l}_{\mathit{kR}}-f_{\mathit{kl}}\left(r\right)\mathrm{.}{l}_{\mathit{kl}}\right)}}+j\underset{J_l\left(r,x\right)}{\underset{\}}{{\displaystyle \underset{k=\mathit{1}}{\overset{3}{\Sigma }}}\left(f_{\mathit{kR}}\left(r\right)\mathrm{.}{l}_{\mathit{kR}}+f_{\mathit{kl}}\left(r\right)\mathrm{.}{l}_{\mathit{kR}}\right)}}$$

What can also be written $$\underset{}{J}\left(r,x\right)=J_R\left(r,x\right)+j{J}_l\left(r,x\right)$$

We thus obtain a relation between the vector of current density induced in the zone considered of the part and the vectors of the currents in the inductors. With on the one hand the impedance matrix linking electrical quantities between inductors, and on the other hand the image functions of current densities in the room, we thus have all the information necessary to calculate the vector of unknowns x from of a determined power density profile. It should be noted that the vector of the capacitors, that is to say the vector of the capacitances of the oscillating circuits, can also be used in this calculation, since these capacitors are generally not strictly equal because of the manufacturing tolerances and they can also drift somewhat. For the calculation, we can use software for solving partial differential equations, with various possible numerical techniques such as finite elements, finite differences, finite volumes, boundary integrals, partial circuit elements, or any other similar technique.

This method has been described for a given example of a relatively simple magnetically coupled system, but is nonetheless transposable to any more complex and non-symmetrical system. The number of reels is not limited, and various shapes and configurations of the coils or parts to be heated are possible, as in the examples visible on the Figures 3 to 6 .

Once the image function of the current density is determined, the image function of the power density D _p ( r, x ) is determined by the relationships of equations (3) and (4) above. It is furthermore advantageous to optimize by calculation the vector of unknowns x . The optimization problem consists of calculating an optimized vector x making it possible to minimize the difference between the image function of the power density and a reference power density function Dp ^ref ( r ) which corresponds to a reference power density profile that we try to inject into the metal disc. This reference power density function takes for example a constant value if we are looking for a temperature homogeneity on the disk. It is however possible to have a non-constant function in order to obtain particular heating profiles. With the equipment of the figure 1 the applicant has carried out tests with different reference power density functions corresponding for example to sinusoidal or triangular profiles in the radial direction of the disk, and the results are very satisfactory.

et $X_i^B$

sur les inconnues recherchées. Cela nous permet d'éliminer entre autres les solutions aberrantes ou qui n'ont pas de réalité physique. La formulation du problème d'optimisation revient donc à minimiser g (r, X) avec x={x ₁,..., x_n } ^T et x_i ∈ └x_i ^B,x_i ^H ┘, i=1,...,n.Optimization therefore consists of minimizing the function g ( r, x ) = | Dp ( r, x ) - Dp ^ref ( r ) | while setting high and low limits $X_i^H$

and $X_i^B$

on the unknowns sought. This allows us to eliminate among other things outliers or that have no physical reality. The formulation of the optimization problem thus amounts to minimizing g (r, X) with x = { x ₁ , ..., x _n } ^T and x _i ∈ └ x _i ^B , x _i ^H ┘, i = 1, ..., n .

After solving the problem, we obtain an optimized vector x containing all the amplitudes of the vectors of the currents in the inductors and their respective phases, for the given metal disk. One of the results for an example of a 650 mm diameter disk, with a power density reference | Dp ^ref | equal to 10MW / m ³ , gives a maximum relative difference of 3% on the image function of the power density as represented Dp ( r, x ) on the figure 7 .

This method of resolution can easily be enlarged to take into account several dimensions of a disk, for example three if in addition to the radius one takes into account the angular position and the thickness of material of the zone considered, while taking into account also the equality of the reactive compensation required at the terminals of each coil so that the three oscillating circuits oscillate at very similar frequencies. We would thus pass from a vector to five unknowns to a vector with eighteen unknowns, without changing the physical system.

The method explained above for the determination of the optimized vector x is advantageously used in the induction heating method according to the invention, this method being able to be implemented in particular in one or the other of the heating devices represented. on the figures 8 and 9 .

On the figure 8 is schematically shown a first embodiment of an induction heating device according to the invention, wherein the supply 1 of the inverters is a DC source.

The heating device comprises inductors Ind1, Ind2,... Indp, magnetically coupled, each inductor being supplied by a current inverter O1, O2,..., Op, which is specific to it and is associated with a capacitor C _1. , C ₂ , ..., Cp, to form an oscillating circuit OC1, OC2, ..., OCp. The inverters of current are put in series with the power supply 1. Each inverter generally comprises bidirectional electronic switches, and is controlled by a control unit also called modulator M1, M2, ..., Mp. Each modulator designs control commands for the switches in the form of pulses, and the offset in time of these commands makes it possible to vary the amplitude A ₁ , A ₂ ,..., A _p , and the phase φ _1. , φ ₂ , ..., φ _p , of the current I ₁ , I ₂ , ..., I _p , passing through the corresponding inductor. The variation of the amplitude of the current output current of each inverter is effected by introducing an offset angle on the signal generated by the modulator controlling the inverter. By choosing a reference inverter as explained below, the offset angles on the other inverters can be introduced with respect to a control angle on the reference inverter. The control on the reference inverter can be carried out for example with a duty cycle equal to 2/3, that is to say a control angle of 30 °.

The oscillating circuits have at least approximately the same resonance frequency, which maximizes the efficiency of the induction since the inductors work substantially at this frequency, and also reduces the losses in the inverters. The periodic control signals of the inverters generated by the modulators therefore have substantially the same frequency. To vary the phase φ ₁ , φ ₂ , ..., φ _p , of a current I ₁ , I ₂ , ..., I _p , passing through an inductor, it suffices to shift the control signal over time. of the corresponding inverter, that is to say to apply the same time offset to all the control commands of the switches of the inverter. The offset can either be late or in advance compared to the control signal of the inverter of another inductor taken as a reference.

To control in real time the power density to be injected into the heated room in order to reach the desired temperature profile, it is necessary to provide means for determining the amplitude and phase parameters of the currents flowing through the inductors in order to be able to correct the control of the inverters. Means for determining the amplitude and phase parameters of currents I ₁ , I ₂ ,..., I _p , inductors, not shown in the figure, are provided to supply these parameters to comparator units ε ₁ , ε ₂ , ..., ε _p . These determination means may consist for example of current transformers each arranged in series with an inductor, but other means are possible. One could for example measure the active current supplied by the inverter to the oscillating circuit, and calculate the current in the inductor using the parameters of inductance and capacitance.

Provision is also made for means for determining an effective temperature profile of the heated metal part 10, not shown in the figure, for example by placing thermocouples on a number n of heated zones and by raising the temperatures θ _{1 mes} , θ _{2 mes} , ..., θ _{n mes} , measured. These temperatures can also be determined using a thermal imaging camera, or can be calculated from the induced currents if, for example, heated zones are too confined for direct measurement.

The effective temperature profile is for example determined continuously during the heating and is regularly compared to a temperature profile of reference θ _{1 ref} , θ _{2 ref} , ..., θ _{n ref} , corresponding to the desired final heating profile for the part and previously entered into a memory. This comparison is performed by a comparator 2, which can integrate said memory. The result is processed by a calculator which, from an equation deduced from the equation of heat and possibly simplified as equation (2) above, calculates the reference power density profile Dp ^ref ₁ , Dp ^ref ₂ , ..., Dp ^ref _n that the heater must inject into the room to reach the reference temperature profile. The computer may consist of a memory in which is entered an array of pre-calculated reference power density profiles corresponding to different actual temperature profiles for one or more room configurations and one or more reference power density profiles.

A calculator establishes the target currents to be delivered by the inverters so that the currents of the inductors reach appropriate target values I _{1 ref} , I _{2 ref} , ..., I _{p ref} , to inject into the part the power density profile of the reference. This computation uses the matrix of impedances Z with the vectorial functions f _k and preferably the vector of the capacities of the oscillating circuits, defined previously. The comparator units ε ₁ , ε ₂ , ..., ε _p compare the measured or calculated current parameters I _{1 mes} , I _{2 mes} , ..., I _{p mes} , inductors to the target values I _{1 ref} , I _{2 ref} , ..., I _{p ref,} and determine the currents deviations δI _{1 corr} , δI _{2 corr} , ..., δI _{p corr} to be corrected, also called correction currents. CORR ₁ , CORR ₂ , ..., CORR _p processing units, amplitude and phase parameters that these correction currents generate correction instructions sent to the modulators to control the inverters so as to correct the amplitudes and the phase shifts of the currents passing through the inductors.

It is understood that by controlling the phase shifts of the currents in the inductors, no attempt is made to obtain a zero or constant phase shift. On the contrary, it is sought to use phase shifts as real-time adjustment parameters of the power density to be injected into the heated room, which is made possible by taking into account the complete impedance matrix as explained in what follows. above. In other words, phase shifts are used as control parameters of the temperature profile. For example, it can be planned to control in time actual phase shifts of the currents in the inductors every quarter period of the control signals of the inverters generated by the modulators, to finely control the temperature according to different profiles, for example a flat profile, or a rising or falling profile linearly (polynomial d order 1) or non-linearly (order polynomial> 1).

Advantageously, it is possible to determine an initial value Z _ini of the impedance matrix Z for an initial average temperature θ _ini of the inductors and of the part to be heated, and then to determine at variable or periodic intervals the modified impedance matrix Z _mod ( θ) for at least one increased value θ _mod of the mean temperature θ, and the modified impedance matrix is used to recalculate the target currents. In the case of variable sampling intervals, the calculation of the target currents can be carried out each time the measured average temperature θ reaches substantially a new increased value θ _mod among a series of predetermined values.

Advantageously, the current inverter supplying the inductor of lower impedance, for example the coil Ind1 in the example of the figure 1 , is chosen as the reference inverter since the current in this inductor, larger than that in the other inductors, is preferably taken as a phase reference. The current inverter having the highest current, or the voltage inverter having the highest voltage in the case where the power supply 1 of the inverters is a voltage source as shown in FIG. figure 9 , can be taken as reference inverter. In addition, the reference inverter can be advantageously adjusted with a duty cycle of 2/3, ie it is controlled so as to generate a square wave of 120 ° ON and 60 ° OFF per half-period. . This aims to cancel the harmonic of order 3 and its multiples in order to reduce the harmonic disturbances created by this inverter on these neighbors. It is understood that the duty cycle of the reference inverter is not necessarily set to 2/3. For example, a command in full wave may be preferred in some cases.

The rms value of the current in the reference inverter can be set by action on the DC supply 1 current or voltage. This has the advantage of having a vector of unknowns (see previous relation 1) in which the phase of the current in the inductor Ind1 has been eliminated, which simplifies obtaining the optimized vector x as in the example described previously. It is understood that one can alternatively adjust the rms value of the current in the reference inverter by introducing offset angles on the control of this inverter. On the figure 8 the current I ₁ being taken as a phase reference, it is advantageous that the corresponding comparator unit ε ₁ receives the parameters of the current I _{c mes} delivered by the continuous supply 1. In this way, the processing unit CORR ₁ associated will be adapted to generate control instructions sent to the power supply 1 via a control modulator M'1, so as to modify the current delivered by the inverter O1 to the oscillating circuit OC1, which makes it possible to control the amplitude of the this current and therefore to change the amplitude of the current I ₁ in inductor Ind1.

1. a) on compare le profil de température effectif de la pièce au profil prédéterminé de température de référence, et on calcule le profil de densité de puissance de référence que le dispositif doit injecter dans la pièce pour atteindre le profil de température de référence ;
2. b) à partir de la matrice d'impédances Z du système, préférablement associée au vecteur des capacités des circuits oscillants, et par la connaissance des fonctions images vectorielles f_k , on calcule les courants cibles que doivent délivrer les onduleurs afin que les courants des inducteurs atteignent les valeurs cibles appropriées pour injecter dans la pièce le profil de densité de puissance de référence ;
3. c) on détermine par mesure ou par calcul les courants traversant les inducteurs pour les comparer aux valeurs cibles de ces courants et déterminer les écarts de courants à corriger, et on envoie aux modulateurs les instructions de correction afin de commander les onduleurs de façon à corriger les courants.

To heat a metal part with the heating device described above, the method comprising the following steps is used:

1. a) comparing the effective temperature profile of the workpiece with the predetermined reference temperature profile, and calculating the reference power density profile that the device is to inject into the workpiece to reach the reference temperature profile;
2. b) from the system impedance matrix Z , preferably associated with the vector of the oscillating circuit capacitors, and by the knowledge of the vector image functions f _k , the target currents to be supplied by the inverters are calculated so that the currents of the Inductors reach the appropriate target values to inject the reference power density profile into the part;
3. c) the currents passing through the inductors are determined by measurement or by calculation to compare them with the target values of these currents and determine the currents to be corrected, and the correction instructions are sent to the modulators in order to control the inverters so as to correct the currents.

Of course, the target currents as well as the currents of the inductors measured or calculated are current vectors, therefore one takes into account not only the amplitude but also the phase.

Advantageously, after successively performing steps (a) and (b), step (c) is carried out at least once to reduce the differences in currents to be corrected, and then steps (a) are repeated at least once, (b) and (c) by updating the actual temperature profile by temperature measurements in different heated areas of the room.

On the figure 9 is schematically shown a second embodiment of an induction heating device according to the invention, wherein the supply 1 of the inverters is a DC voltage source.

The heating device is similar to that of the first embodiment of the figure 8 , but the current inverters are paralleled with the voltage source. This embodiment has certain advantages, in particular that of reducing conduction losses in the inverters. On the other hand, the current parameter I _{c calc} representative of the current delivered by the power supply 1 to the inverter O1 must be calculated from the supply voltage by means of an impedance matrix Z '.

Claims (10)

1. Induction heating method implemented in a device for heating a metal part, the device including magnetically coupled inductors (Indl, Ind2,..., Indp), each inductor being powered by a dedicated inverter (O1, O2,..., Op) associated with a capacitor (C1, C2,..., Cp) such as to form an oscillating circuit (OC1, OC2,..., OCp), said oscillating circuits having at least approximately the same resonance frequency, each inverter being controlled by a control unit (M1, M2,..., Mp) such as to vary the amplitude (A₁, A₂,..., Ap) and the phase (ϕ₁, ϕ₂,..., ϕ_p) of the current (I₁, I₂,..., I_p) passing through the corresponding inductor, the device also including means for determining said current (I₁, I₂,..., I_p) as well as means for determining an actual temperature profile (θ_{1 mes}, θ_{2 mes}, ..., θ_{n mes}) of said metal part, said method including the following steps:

   a) comparing said actual temperature profile (θ_{1 mes}, θ_{2 mes}, ..., θ_{n mes}) with a reference temperature profile (θ_{1 ref}, θ_{2 ref}, ..., θ_{n ref}) and calculating a profile of the reference power density (Dp^ref ₁, Dp^ref ₂,..., Dp^ref _n) which the heating device must inject into said part in order to achieve said reference temperature profile;

   b) from a matrix of impedances (Z) determined by knowledge of the electromagnetic relationships linking said inductors with each other and with said part and by knowledge of vector image functions (f_k ) representing the relationships between the current densities created by the inductors and the currents (I₁, I₂,..., I_p) passing through the inductors, calculating the target currents which the inverters must produce in order for the currents of the inductors to reach target values (I₁ ref, I_{2 ref},..., I_{p ref}) that are suitable for injecting said reference power density profile (Dp^ref ₁, Dp^ref ₂,..., Dp^ref _n, ) into said part;

   c) determining the currents (I_{1 mes}, I_{2 mes},..., I_{p mes}) passing through the inductors in order to compare them with said target values (I_{1 ref}, I_{2 ref},..., I_{p ref}) and to determine current deviations (θI_{1 corr}, δI_{2 corr},..., δI_{p corr}) to be corrected, and sending correction instructions to said control units (M1, M2,..., Mp) in accordance with said current deviations in order to control the inverters such as to correct the currents passing through the inductors.
2. Heating method according to claim 1, in which the capacitances of said capacitors (C1, C2,..., Cp) are determined, and said matrix of impedances (Z) is associated with a vector (C) of the capacitances.
3. Heating method according to claim 1 or 2, in which the initial value (Z _ini ) of said matrix of impedances (Z) is determined for a given initial average temperature (θ_ini) of said inductors and of said part, then the matrix of impedances (Z _mod (θ)) modified for at least one increased value (θ _mod ) of said average temperature is determined at variable or periodic intervals, and said modified matrix of impedances is used for recalculating said target values (I_{1 ref}, I_{2 ref},..., I_{p ref}).
4. Heating method according to any one of claims 1 to 3, in which after having successively carried out steps (a) and (b), step (c) is carried out at least once in order to reduce the current deviations (δI_{1 corr}, δI_{2 corr},..., δI_{p corr}) to be corrected, then steps (a), (b) and (c) are reiterated at least once on updating said actual temperature profile (θ_{1 mes}, θ_{2 mes}, ..., θ_{n mes}) with temperature measurements in different heated zones of the part.
5. Heating method according to any one of claims 1 to 4, in which for the determination by calculation of said target values (I_{1 ref}, I_{2 ref},..., I_{p ref}) in step (b), because of knowledge of said vector image functions (f_k ), image functions (Dp(r,x)) of the power densities are calculated according to the spatial characteristics (r) of the zones of the part into which said power densities are injected, and an optimized vector (x) of the target currents to be determined is calculated by minimizing the difference between each of said image functions of the power densities (Dp(r,x)) and a reference power density function (Dp^ref(r)) corresponding to said reference power density profile (Dp^ref ₁, Dp^ref ₂,..., Dp^ref _n,).
6. Heating method according to any one of claims 1 to 5, in which an inverter (O1) having, in comparison with the other inverters (O2,..., Op), the highest current in the case of a current inverter or the highest voltage in the case of a voltage inverter is chosen as the reference inverter and shift angles are introduced in the controls of the other inverters with respect to a control angle of the reference inverter.
7. Heating method according to claim 6, in which the reference inverter (O1) is adjusted with a duty cycle equal to 2/3, in order to reduce the harmonic interference created by this inverter on its neighbours (O2,..., Op).
8. Heating method according to claim 6 or 7, in which the RMS value of the current in said reference inverter (O1) is adjusted by acting on a DC power supply (1) which powers the inverters (O1, O2,..., Op).
9. Induction heating device comprising:

   magnetically coupled inductors (Ind1, Ind2,..., Indp), each inductor being associated with a capacitor (C1, C2,..., Cp) in order to form an oscillating circuit (OC1, OC2,..., OCp), said oscillating circuits having at least approximately the same resonance frequency;

   inverters (O1, O2,..., Op), each powering a dedicated inductor (Ind1, Ind2,..., Indp), each inverter being controlled by a control unit (M1, M2,..., Mp) in such a way as to vary the amplitude (A₁, A₂,..., Ap) and the phase (ϕ₁, ϕ₂,..., ϕ_p) of the current (I₁, I₂,..., Ip) passing through the corresponding inductor;

   characterized in that it comprises moreover:

   means of determination of the currents (I₁, I₂,..., I_p) passing through the inductors as well as means of determination of an actual temperature profile (θ_{1 mes}, θ_{2 mes}, ..., θ_{n mes}) of a metal part heated by the device;

   means of comparison of said actual temperature profile (θ_{1 mes}, θ_{2 mes}, ..., θ_{n mes}) with respect to a reference temperature profile (θ_{1 ref}, θ_{2 ref}, ..., θ_{n ref});

   means of calculating a reference power density profile (Dp^ref ₁, Dp^ref ₂,..., Dp^ref _n) that the heating device must inject into said part in order to achieve said reference temperature profile;

   means of calculating, based on knowledge of a matrix of the impedances (Z), target currents that the inverters must deliver in order that the inductor currents reach appropriate target values (I_{1 ref}, I_{2 ref},..., I_{p ref}) for injecting said reference power density profile (Dp^ref ₁, Dp^ref ₂,..., Dp^ref _n, ) into said part;

   means of comparison (ε₁, ε₂,..., ε_p) of the currents (I_{1 mes}, I_{2 mes},..., I_{p mes}) passing through the inductors with respect to said target values (I_{1 ref}, I_{2 ref},..., I_{p ref}), capable of determining current deviations (δI_{1 corr}, δI_{2 corr},..., δI_{p corr}) to be corrected, and means of processing (CORR₁, CORR₂,..., CORR_p) said current deviations capable of generating correction instructions sent to said control units (M1, M2,..., Mp) for controlling the inverters in such a way as to correct the currents passing through the inductors.
10. Induction heating device according to claim 9, in which the inverters (O1, O2,..., Op) are powered by the same current source or voltage source power supply (1), and in which said means of comparison of said determined currents (I_{1 mes}, I_{2 mes},..., Ip _mes) passing through the inductors include comparator units (ε₁, ε₂,..., ε_p) each receiving determined parameters (A₁, ϕ₁; A₂, ϕ₂;...; A_p , ϕ_p) of a current (I_{1 mes}, I_{2 mes},..., Ip _mes) passing through an inductor and parameters of the corresponding target values (I_{1 ref}, I_{2 ref},..., I_{p ref}) and each being connected to a unit (CORR₁, CORR₂,..., CORR_p) for processing said current deviations, one (ε₁) of said comparator units furthermore receiving parameters (I_{c mes}, I_{c calc}) representative of what said power supply (1) delivers and its associated processing unit (CORR₁) being adapted to generate regulation instructions sent to said power supply (1) in order to modify the current or the voltage that it delivers.

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